TY - JOUR

T1 - Geometrically nonlinear modelling of pre-stressed viscoelastic fibre-reinforced composites with application to arteries

AU - Tagiltsev, I. I.

AU - Shutov, A.

N1 - Publisher Copyright: © 2020, Springer-Verlag GmbH Germany, part of Springer Nature. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021/2

Y1 - 2021/2

N2 - Mechanical behaviour of pre-stressed fibre-reinforced composites is modelled in a geometrically exact setting. A general approach which includes two different reference configurations is employed: one configuration corresponds to the load-free state of the structure and another one to the stress-free state of each material particle. The applicability of the approach is demonstrated in terms of a viscoelastic material model; both the matrix and the fibre are modelled using a multiplicative split of the deformation gradient tensor; a transformation rule for initial conditions is elaborated and specified. Apart from its simplicity, an important advantage of the approach is that well-established numerical algorithms can be used for pre-stressed inelastic structures. The interrelation between the advocated approach and the widely used "opening angle" approach is clarified. A full-scale FEM simulation confirms the main predictions of the "opening angle" approach. A locking effect is discovered: in some cases the opening angle of the composite is essentially smaller than the opening angles of its individual layers. Thus, the standard cutting test typically used to analyse pre-stresses does not carry enough information and more refined experimental techniques are needed.

AB - Mechanical behaviour of pre-stressed fibre-reinforced composites is modelled in a geometrically exact setting. A general approach which includes two different reference configurations is employed: one configuration corresponds to the load-free state of the structure and another one to the stress-free state of each material particle. The applicability of the approach is demonstrated in terms of a viscoelastic material model; both the matrix and the fibre are modelled using a multiplicative split of the deformation gradient tensor; a transformation rule for initial conditions is elaborated and specified. Apart from its simplicity, an important advantage of the approach is that well-established numerical algorithms can be used for pre-stressed inelastic structures. The interrelation between the advocated approach and the widely used "opening angle" approach is clarified. A full-scale FEM simulation confirms the main predictions of the "opening angle" approach. A locking effect is discovered: in some cases the opening angle of the composite is essentially smaller than the opening angles of its individual layers. Thus, the standard cutting test typically used to analyse pre-stresses does not carry enough information and more refined experimental techniques are needed.

KW - Pre-stresses

KW - Finite strain viscoelasticity

KW - Fibre-reinforced composites

KW - Cutting test

KW - Opening angle approach

KW - Efficient numerics

KW - FINITE-ELEMENT MODEL

KW - RESIDUAL-STRESSES

KW - STRAINS

KW - GROWTH

KW - SIMULATION

KW - DAMAGE

UR - http://www.scopus.com/inward/record.url?scp=85091915196&partnerID=8YFLogxK

UR - https://arxiv.org/abs/2006.08719v1

U2 - 10.1007/s10237-020-01388-3

DO - 10.1007/s10237-020-01388-3

M3 - Article

C2 - 33011868

VL - 20

SP - 323

EP - 337

JO - Biomechanics and Modeling in Mechanobiology

JF - Biomechanics and Modeling in Mechanobiology

SN - 1617-7959

IS - 1

ER -